A generalization of n -ary prime subhypermodule

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Abstract
Let ( M, f, g ) be an ( m, n )-hypermodule over an ( m, n )-hyperring ( R, h, k ). A proper subhypermodule N of M is called n -ary 2-absorbing subhypermodule if whenever g ( r 1 n− 1 , m ) ⊆ N for some r 1 n− 1 ∈ R and m ∈ M , then either g ( r 1 n −1 , M ) ⊆ N or g ( r i , m , 1 R ( n −2) ) ⊆ N for some i ∈ {1, . . ., n − 1}. Various properties of n -ary 2-absorbing subhy-permodules are investigated. In particular, it is shown that if N is a subhypermodule of an ( m, n )-hypermodule ( M, f, g ) over an ( m, n )- hyperring ( R, h, k ), then N is n -ary 2-absorbing if and only if whenever g(I 1 , I 2 , 1 R ( n −3) , L ) ⊆ N for some hyperideals I 1 , I 2 of R and subhyper- module L of M , then either g ( I 1 , I 2 , 1 R (n−3) , M ) ⊆ N or g ( I 1 , 1 R ( n −2) , L ) ⊆ N or g ( I 2 , 1 R ( n −2) , L ) ⊆ N . Also, n -ary 2-absorbing subhypermodules in multiplication ( m, n )-hypermodules are studied.

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